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        <span class="post-time"> 0001-01-01 </span>
        
        
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  <ul>
    <li><a href="#密码脱落n-最长回文子串">密码脱落（n-最长回文子串）</a>
      <ul>
        <li><a href="#题意">题意</a></li>
        <li><a href="#思路">思路</a></li>
      </ul>
    </li>
    <li><a href="#括号配对">括号配对</a>
      <ul>
        <li><a href="#题意-1">题意</a></li>
        <li><a href="#思路-1">思路</a></li>
        <li><a href="#代码">代码</a></li>
      </ul>
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    <div class="post-content">
      <h1 id="密码脱落n-最长回文子串">密码脱落（n-最长回文子串）</h1>
<h2 id="题意">题意</h2>
<p>字符串中会脱落其中几个字符，给你脱落之后的字符串，问：若原子串为回文子串，那么脱落几个子串。增加几个字符成为回文子串。</p>
<h2 id="思路">思路</h2>
<p>往回文子串靠，回文子串去掉几个字符，剩下的字符串。相当于求出剩下的字符串最长回文子串f[0] [n],答案为n-f[0] [n],不属于最长回文子串的字符，我们都可以补上于之匹配。</p>
<p>求回文子串，用dp</p>
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<td class="lntd">
<pre class="chroma"><code class="language-cpp" data-lang="cpp"><span class="cp">#pragma comment(linker, &#34;/STACK:1024000000,1024000000&#34;)
</span><span class="cp">#include</span><span class="cpf">&lt;cstdio&gt;</span><span class="cp">
</span><span class="cp">#include</span><span class="cpf">&lt;cstring&gt;</span><span class="cp">
</span><span class="cp">#include</span><span class="cpf">&lt;algorithm&gt;</span><span class="cp">
</span><span class="cp">#include</span><span class="cpf">&lt;iostream&gt;</span><span class="cp">
</span><span class="cp">#include</span><span class="cpf">&lt;string&gt;</span><span class="cp">
</span><span class="cp">#include</span><span class="cpf">&lt;vector&gt;</span><span class="cp">
</span><span class="cp">#include</span><span class="cpf">&lt;stack&gt;</span><span class="cp">
</span><span class="cp">#include</span><span class="cpf">&lt;bitset&gt;</span><span class="cp">
</span><span class="cp">#include</span><span class="cpf">&lt;cstdlib&gt;</span><span class="cp">
</span><span class="cp">#include</span><span class="cpf">&lt;cmath&gt;</span><span class="cp">
</span><span class="cp">#include</span><span class="cpf">&lt;set&gt;</span><span class="cp">
</span><span class="cp">#include</span><span class="cpf">&lt;list&gt;</span><span class="cp">
</span><span class="cp">#include</span><span class="cpf">&lt;deque&gt;</span><span class="cp">
</span><span class="cp">#include</span><span class="cpf">&lt;map&gt;</span><span class="cp">
</span><span class="cp">#include</span><span class="cpf">&lt;queue&gt;</span><span class="cp">
</span><span class="cp"></span><span class="k">using</span> <span class="k">namespace</span> <span class="n">std</span><span class="p">;</span>
<span class="k">typedef</span> <span class="kt">long</span> <span class="kt">long</span> <span class="n">ll</span><span class="p">;</span>
<span class="k">typedef</span> <span class="kt">unsigned</span> <span class="kt">long</span> <span class="kt">long</span> <span class="n">ull</span><span class="p">;</span>
<span class="cp">#define mst(s,_s) memset(s, _s, sizeof(s))
</span><span class="cp"></span><span class="k">const</span> <span class="kt">double</span> <span class="n">PI</span> <span class="o">=</span> <span class="n">acos</span><span class="p">(</span><span class="o">-</span><span class="mf">1.0</span><span class="p">);</span>
<span class="k">const</span> <span class="kt">double</span> <span class="n">eps</span> <span class="o">=</span> <span class="mf">1e-6</span><span class="p">;</span>
<span class="k">const</span> <span class="kt">int</span> <span class="n">INF</span> <span class="o">=</span> <span class="mh">0x3f3f3f3f</span><span class="p">;</span>
<span class="k">const</span> <span class="kt">int</span> <span class="n">N</span> <span class="o">=</span> <span class="mf">1e3</span><span class="o">+</span><span class="mi">100</span><span class="p">;</span>
<span class="kt">int</span> <span class="n">T</span><span class="p">,</span><span class="n">n</span><span class="p">,</span><span class="n">m</span><span class="p">;</span>

<span class="kt">int</span> <span class="n">f</span><span class="p">[</span><span class="n">N</span><span class="p">][</span><span class="n">N</span><span class="p">];</span>

<span class="n">string</span> <span class="n">str</span><span class="p">;</span>

<span class="kt">int</span> <span class="nf">main</span><span class="p">()</span> <span class="p">{</span>
    <span class="n">cin</span><span class="o">&gt;&gt;</span><span class="n">str</span><span class="p">;</span>
    <span class="n">n</span><span class="o">=</span><span class="n">str</span><span class="p">.</span><span class="n">length</span><span class="p">();</span>
    <span class="k">for</span><span class="p">(</span><span class="kt">int</span> <span class="n">len</span><span class="o">=</span><span class="mi">1</span><span class="p">;</span><span class="n">len</span><span class="o">&lt;=</span><span class="n">n</span><span class="p">;</span><span class="n">len</span><span class="o">++</span><span class="p">)</span>
    <span class="p">{</span>
        
        <span class="k">for</span><span class="p">(</span><span class="kt">int</span> <span class="n">l</span><span class="o">=</span><span class="mi">0</span><span class="p">;</span><span class="n">l</span><span class="o">+</span><span class="n">len</span><span class="o">-</span><span class="mi">1</span><span class="o">&lt;</span><span class="n">n</span><span class="p">;</span><span class="n">l</span><span class="o">++</span><span class="p">)</span>
        <span class="p">{</span>
            <span class="kt">int</span> <span class="n">r</span><span class="o">=</span><span class="n">l</span><span class="o">+</span><span class="n">len</span><span class="o">-</span><span class="mi">1</span><span class="p">;</span>
            <span class="k">if</span><span class="p">(</span><span class="n">len</span><span class="o">==</span><span class="mi">1</span><span class="p">)</span>
            <span class="p">{</span>
                <span class="n">f</span><span class="p">[</span><span class="n">l</span><span class="p">][</span><span class="n">r</span><span class="p">]</span><span class="o">=</span><span class="mi">1</span><span class="p">;</span>
            <span class="p">}</span>
            <span class="k">else</span><span class="p">{</span>
                <span class="k">if</span><span class="p">(</span><span class="n">str</span><span class="p">[</span><span class="n">l</span><span class="p">]</span><span class="o">==</span><span class="n">str</span><span class="p">[</span><span class="n">r</span><span class="p">])</span>  <span class="n">f</span><span class="p">[</span><span class="n">l</span><span class="p">][</span><span class="n">r</span><span class="p">]</span><span class="o">=</span><span class="n">max</span><span class="p">(</span><span class="n">f</span><span class="p">[</span><span class="n">l</span><span class="p">][</span><span class="n">r</span><span class="p">],</span><span class="n">f</span><span class="p">[</span><span class="n">l</span><span class="o">+</span><span class="mi">1</span><span class="p">][</span><span class="n">r</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">+</span> <span class="mi">2</span><span class="p">);</span>
                <span class="n">f</span><span class="p">[</span><span class="n">l</span><span class="p">][</span><span class="n">r</span><span class="p">]</span><span class="o">=</span><span class="n">max</span><span class="p">(</span><span class="n">f</span><span class="p">[</span><span class="n">l</span><span class="p">][</span><span class="n">r</span><span class="p">],</span><span class="n">f</span><span class="p">[</span><span class="n">l</span><span class="o">+</span><span class="mi">1</span><span class="p">][</span><span class="n">r</span><span class="p">]);</span>
                <span class="n">f</span><span class="p">[</span><span class="n">l</span><span class="p">][</span><span class="n">r</span><span class="p">]</span><span class="o">=</span><span class="n">max</span><span class="p">(</span><span class="n">f</span><span class="p">[</span><span class="n">l</span><span class="p">][</span><span class="n">r</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span><span class="n">f</span><span class="p">[</span><span class="n">l</span><span class="p">][</span><span class="n">r</span><span class="p">]);</span>
            <span class="p">}</span>
            
            
        <span class="p">}</span>
    <span class="p">}</span>
    <span class="n">cout</span><span class="o">&lt;&lt;</span><span class="n">n</span><span class="o">-</span><span class="n">f</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="n">n</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="o">&lt;&lt;</span><span class="n">endl</span><span class="p">;</span>
    <span class="k">return</span> <span class="mi">0</span><span class="p">;</span>
<span class="p">}</span>

</code></pre></td></tr></table>
</div>
</div><h1 id="括号配对">括号配对</h1>
<h2 id="题意-1">题意</h2>
<p>递归定义一组字符匹配模式</p>
<p>增加几个字符满足这个匹配。</p>
<p><img src="https://tva1.sinaimg.cn/large/007S8ZIlly1gjh2lypzsij30u011ctes.jpg" alt="image-20201007210347985"></p>
<h2 id="思路-1">思路</h2>
<p>添加多少个字符，可以转化为n-“回文子串”，这里的回文子串需要重新定义</p>
<p>AAAABBBB：A符合定义，B也符合定义的话：最长子串，我们枚举中间端点取最大值。</p>
<p>ABBA：这种情况，我们判断【l， r】 match（l,r)是不是匹配，匹配的话f（l+1，r-1）+2</p>
<h2 id="代码">代码</h2>
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<td class="lntd">
<pre class="chroma"><code class="language-cpp" data-lang="cpp"><span class="cp">#pragma comment(linker, &#34;/STACK:1024000000,1024000000&#34;)
</span><span class="cp">#include</span><span class="cpf">&lt;cstdio&gt;</span><span class="cp">
</span><span class="cp">#include</span><span class="cpf">&lt;cstring&gt;</span><span class="cp">
</span><span class="cp">#include</span><span class="cpf">&lt;algorithm&gt;</span><span class="cp">
</span><span class="cp">#include</span><span class="cpf">&lt;iostream&gt;</span><span class="cp">
</span><span class="cp">#include</span><span class="cpf">&lt;string&gt;</span><span class="cp">
</span><span class="cp">#include</span><span class="cpf">&lt;vector&gt;</span><span class="cp">
</span><span class="cp">#include</span><span class="cpf">&lt;stack&gt;</span><span class="cp">
</span><span class="cp">#include</span><span class="cpf">&lt;bitset&gt;</span><span class="cp">
</span><span class="cp">#include</span><span class="cpf">&lt;cstdlib&gt;</span><span class="cp">
</span><span class="cp">#include</span><span class="cpf">&lt;cmath&gt;</span><span class="cp">
</span><span class="cp">#include</span><span class="cpf">&lt;set&gt;</span><span class="cp">
</span><span class="cp">#include</span><span class="cpf">&lt;list&gt;</span><span class="cp">
</span><span class="cp">#include</span><span class="cpf">&lt;deque&gt;</span><span class="cp">
</span><span class="cp">#include</span><span class="cpf">&lt;map&gt;</span><span class="cp">
</span><span class="cp">#include</span><span class="cpf">&lt;queue&gt;</span><span class="cp">
</span><span class="cp"></span><span class="k">using</span> <span class="k">namespace</span> <span class="n">std</span><span class="p">;</span>
<span class="k">typedef</span> <span class="kt">long</span> <span class="kt">long</span> <span class="n">ll</span><span class="p">;</span>
<span class="k">typedef</span> <span class="kt">unsigned</span> <span class="kt">long</span> <span class="kt">long</span> <span class="n">ull</span><span class="p">;</span>
<span class="cp">#define mst(s,_s) memset(s, _s, sizeof(s))
</span><span class="cp"></span><span class="k">const</span> <span class="kt">double</span> <span class="n">PI</span> <span class="o">=</span> <span class="n">acos</span><span class="p">(</span><span class="o">-</span><span class="mf">1.0</span><span class="p">);</span>
<span class="k">const</span> <span class="kt">double</span> <span class="n">eps</span> <span class="o">=</span> <span class="mf">1e-6</span><span class="p">;</span>
<span class="k">const</span> <span class="kt">int</span> <span class="n">INF</span> <span class="o">=</span> <span class="mh">0x3f3f3f3f</span><span class="p">;</span>
<span class="k">const</span> <span class="kt">int</span> <span class="n">N</span> <span class="o">=</span> <span class="mf">1e3</span><span class="o">+</span><span class="mi">100</span><span class="p">;</span>
<span class="kt">int</span> <span class="n">T</span><span class="p">,</span><span class="n">n</span><span class="p">,</span><span class="n">m</span><span class="p">;</span>

<span class="kt">char</span> <span class="n">str</span><span class="p">[</span><span class="n">N</span><span class="p">];</span>
<span class="kt">int</span> <span class="n">f</span><span class="p">[</span><span class="n">N</span><span class="p">][</span><span class="n">N</span><span class="p">];</span>

<span class="kt">bool</span> <span class="nf">match</span><span class="p">(</span><span class="kt">char</span> <span class="n">a</span><span class="p">,</span><span class="kt">char</span> <span class="n">b</span><span class="p">)</span>
<span class="p">{</span>
    <span class="k">if</span><span class="p">(</span><span class="n">a</span><span class="o">==</span><span class="sc">&#39;(&#39;</span> <span class="o">&amp;&amp;</span> <span class="n">b</span><span class="o">==</span><span class="sc">&#39;)&#39;</span><span class="p">)</span> <span class="k">return</span> <span class="nb">true</span><span class="p">;</span>
    <span class="k">if</span><span class="p">(</span><span class="n">a</span><span class="o">==</span><span class="sc">&#39;[&#39;</span> <span class="o">&amp;&amp;</span> <span class="n">b</span><span class="o">==</span><span class="sc">&#39;]&#39;</span><span class="p">)</span> <span class="k">return</span> <span class="nb">true</span><span class="p">;</span>
    <span class="k">else</span> <span class="k">return</span> <span class="nb">false</span><span class="p">;</span>
<span class="p">}</span>

<span class="kt">int</span> <span class="nf">main</span><span class="p">()</span> <span class="p">{</span>
    <span class="n">cin</span><span class="o">&gt;&gt;</span><span class="n">str</span><span class="o">+</span><span class="mi">1</span><span class="p">;</span>
    <span class="n">n</span><span class="o">=</span><span class="n">strlen</span><span class="p">(</span><span class="n">str</span><span class="o">+</span><span class="mi">1</span><span class="p">);</span>
    
    <span class="k">for</span><span class="p">(</span><span class="kt">int</span> <span class="n">len</span><span class="o">=</span><span class="mi">2</span><span class="p">;</span><span class="n">len</span><span class="o">&lt;=</span><span class="n">n</span><span class="p">;</span><span class="n">len</span><span class="o">++</span><span class="p">)</span>
    <span class="p">{</span>
        <span class="k">for</span><span class="p">(</span><span class="kt">int</span> <span class="n">l</span><span class="o">=</span><span class="mi">1</span><span class="p">;</span><span class="n">l</span><span class="o">+</span><span class="n">len</span><span class="o">-</span><span class="mi">1</span><span class="o">&lt;=</span><span class="n">n</span><span class="p">;</span><span class="n">l</span><span class="o">++</span><span class="p">)</span>
        <span class="p">{</span>
            <span class="kt">int</span> <span class="n">r</span><span class="o">=</span><span class="n">l</span><span class="o">+</span><span class="n">len</span><span class="o">-</span><span class="mi">1</span><span class="p">;</span>
            <span class="k">if</span><span class="p">(</span><span class="n">len</span><span class="o">==</span><span class="mi">1</span><span class="p">)</span> <span class="n">f</span><span class="p">[</span><span class="n">l</span><span class="p">][</span><span class="n">r</span><span class="p">]</span><span class="o">=</span><span class="mi">0</span><span class="p">;</span>
            <span class="k">if</span><span class="p">(</span><span class="n">match</span><span class="p">(</span><span class="n">str</span><span class="p">[</span><span class="n">l</span><span class="p">],</span><span class="n">str</span><span class="p">[</span><span class="n">r</span><span class="p">]))</span> <span class="n">f</span><span class="p">[</span><span class="n">l</span><span class="p">][</span><span class="n">r</span><span class="p">]</span><span class="o">=</span><span class="n">max</span><span class="p">(</span><span class="n">f</span><span class="p">[</span><span class="n">l</span><span class="p">][</span><span class="n">r</span><span class="p">],</span><span class="n">f</span><span class="p">[</span><span class="n">l</span><span class="o">+</span><span class="mi">1</span><span class="p">][</span><span class="n">r</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">+</span> <span class="mi">2</span><span class="p">);</span>
            <span class="k">for</span><span class="p">(</span><span class="kt">int</span> <span class="n">k</span><span class="o">=</span><span class="n">l</span><span class="p">;</span><span class="n">k</span><span class="o">&lt;</span><span class="n">r</span><span class="p">;</span><span class="n">k</span><span class="o">++</span><span class="p">)</span>
            <span class="p">{</span>
               <span class="n">f</span><span class="p">[</span><span class="n">l</span><span class="p">][</span><span class="n">r</span><span class="p">]</span><span class="o">=</span><span class="n">max</span><span class="p">(</span><span class="n">f</span><span class="p">[</span><span class="n">l</span><span class="p">][</span><span class="n">r</span><span class="p">],</span><span class="n">f</span><span class="p">[</span><span class="n">l</span><span class="p">][</span><span class="n">k</span><span class="p">]</span><span class="o">+</span><span class="n">f</span><span class="p">[</span><span class="n">k</span><span class="o">+</span><span class="mi">1</span><span class="p">][</span><span class="n">r</span><span class="p">]);</span>
            <span class="p">}</span>
        <span class="p">}</span>
    <span class="p">}</span>
    <span class="n">cout</span><span class="o">&lt;&lt;</span><span class="n">n</span> <span class="o">-</span> <span class="n">f</span><span class="p">[</span><span class="mi">1</span><span class="p">][</span><span class="n">n</span><span class="p">]</span><span class="o">&lt;&lt;</span><span class="n">endl</span><span class="p">;</span>
    <span class="k">return</span> <span class="mi">0</span><span class="p">;</span>
<span class="p">}</span>
</code></pre></td></tr></table>
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